7 - Phonons, maxons and rotons

Summary

In this chapter, we review the high-resolution neutron-scattering data for the dynamic structure factor S(Q, ω) and suggest an interpretation within a unified picture of the excitations in liquid ⁴He consistent with the ideas of Chapter 5. We argue that the phonons (0.1 ≲ Q ≲ 0.7 Å^–1) in the collisionless region and rotons (Q ∼ 1.9 Å^–1) are really two separate branches of the density fluctuation spectrum in the superfluid phase which are hybridized by the condensate. The low-wavevector phonon is interpreted as a zero sound collective density fluctuation while the large-Q maxon–roton is interpreted as a strongly renormalized single-particle excitation. In the intermediate-wavevector region 0.8 ≲ Q ≲ 1.2 Å^–1, we argue that there is evidence that both excitation branches, a sharp single-particle (or atomic-like) maxon excitation and a broad high-energy zero sound phonon, are observed in S(Q, ω). Within this scenario, the appearance of the sharp maxon-roton resonance (0.8 ≲ Q ≲ 2.4 Å^–1) in S(Q, ω) below the superfluid transition temperature Tλ is direct dynamical evidence for the Bose broken symmetry and the associated Bose condensate in superfluid ⁴He.

In Section 7.1, we review the neutron-scattering intensity data for small, intermediate and large wavevectors. In Section 7.2, these results are interpreted starting from the assumption that superfluid He is a Bose-condensed liquid. The condensate inevitably leads to a mixing of the single-particle spectrum described by G_αβ(Q, ω) and the density fluctuation spectrum described by S(Q, ω).